Finite Group Databasebeta

← C29×#19562 #20314462

Subgroups — C29×#19562 #20314462

Order 7424.

574 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3246C211yesmaximal, characteristic
2C29×#3235C211yesmaximal, characteristic
3C29×#3231C211yesmaximal, characteristic, complemented
4C29×#2979C211yesmaximal, characteristic
5C29×#1703C211yesmaximal, characteristic, complemented
6C29×#1699C211yesmaximal, characteristic, complemented
7C29×#1695C211yesmaximal, characteristic, complemented
8C29×#1691C211yesmaximal, characteristic, complemented
9C29×#1683C211yesmaximal, characteristic, complemented
10C29×#1679C211yesmaximal, characteristic, complemented
11C29×#1675C211yesmaximal, characteristic, complemented
12C29×#1671C211yesmaximal, characteristic, complemented
13C29×#1573C211yesmaximal, characteristic, complemented
14C29×#1554C211yesmaximal, characteristic, complemented
15C29×#1542C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C29×#533C2211yescharacteristic
18C29×#532C2211yescharacteristic
19C29×#501—21no—
20C29×#500C2211yescharacteristic
21C29×#498C2211yescharacteristic
22C29×#490—21no—
23C29×#487C2211yescharacteristic
24C29×#487C2211yescharacteristic
25C29×#485—21no—
26C29×#485—21no—
27C29×#482—21no—
28C29×#482—21no—
29C29×#479—21no—
30C29×#479—21no—
31C29×#476C2211yescharacteristic
32C29×#476C2211yescharacteristic
33C29×#476C2211yescharacteristic
34C29×#476C2211yescharacteristic
35C29×#475—21no—
36C29×#474C2211yescharacteristic
37C29×#474C2211yescharacteristic
38C29×#465—21no—
39C29×#465—21no—
40C29×#461C2211yescharacteristic
41C29×#461C2211yescharacteristic
42C29×#460—21no—
43C29×#436—21no—
44C29×#436C2211yescharacteristic
45C29×#436C2211yescharacteristic
46C8×D4×C29—21no—
47C8×D4×C29C2211yescharacteristic
48C8×D4×C29C2211yescharacteristic
49C29×#432C2211yescharacteristic
50C29×#431C2211yescharacteristic
51C29×#431C2211yescharacteristic
52C2×C29×C4⋊C8C2211yescharacteristic
53C29×#408—21no—
54C29×#408—21no—
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#333C2211yescharacteristic
62C29×#333C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#332C2211yescharacteristic
66C29×#332C2211yescharacteristic
67C2×#41×C29—21no—
68C2×SD16×C29—21no—
69C2×SD16×C29—21no—
70C2×M16×C29—21no—
71C2×M16×C29—21no—
72C22×C8×C29—21no—
73C22×C8×C29—21no—
74C22×C8×C29—21no—
75C29×C4⋊Q8D411yescharacteristic
76C29×C4⋊Q8C2311yescharacteristic
77C29×C4⋊Q8C2311yescharacteristic
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×#127D411yescharacteristic
81C29×#125—21no—
82C29×#125—21no—
83C29×#124—21no—
84C29×C22⋊Q8—21no—
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8—21no—
87C29×C22⋊Q8—21no—
88C29×#121—21no—
89C29×#121D411yescharacteristic
90C29×#121D411yescharacteristic
91C4×Q8×C29—21no—
92C4×Q8×C29—21no—
93C4×Q8×C29—21no—
94C4×Q8×C29—21no—
95C4×D4×C29—21no—
96C4×D4×C29C2311yescharacteristic
97C4×D4×C29C2311yescharacteristic
98C29×#117—21no—
99C29×#117—21no—
100C2×C42×C29C2311yescharacteristic
101C29×#107—21no—
102C29×#107—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#106—21no—
106C29×#106—21no—
107C29×#106—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×#106—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8D411yescharacteristic
113C29×C4⋊C8D411yescharacteristic
114C29×C4⋊C8C2311yescharacteristic
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×#103—21no—
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#102—21no—
127C29×#102—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×C22⋊C8—21no—
133C29×C22⋊C8—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8—21no—
136C29×C22⋊C8—21no—
137C29×C22⋊C8—21no—
138C29×C22⋊C8D411yescharacteristic
139C29×C22⋊C8D411yescharacteristic
140C29×#97—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—81no—
145#41×C29—81no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29C2×D411yescharacteristic
156C2×D4×C29C2×D411yescharacteristic
157C22×C4×C29—21no—
158C22×C4×C29—21no—
159C22×C4×C29C2×D411yescharacteristic
160C22×C4×C29C2×D411yescharacteristic
161C22×C4×C29#4111yescharacteristic
162SD16×C29—81no—
163SD16×C29—81no—
164M16×C29—81no—
165M16×C29—81no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—81no—
173C2×C8×C29—81no—
174C2×C8×C29—81no—
175C2×C8×C29C2×D411yescharacteristic
176C2×C8×C29C2×D411yescharacteristic
177C2×C8×C29C2×D411yescharacteristic
178C2×C8×C29C2×D411yescharacteristic
179C4⋊C4×C29—21no—
180C4⋊C4×C29—21no—
181C4⋊C4×C29—21no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—41no—
189C4⋊C4×C29—41no—
190C4⋊C4×C29—41no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29C2×D411yescharacteristic
193C4⋊C4×C29C2×D411yescharacteristic
194C22⋊C4×C29—21no—
195C22⋊C4×C29—21no—
196C22⋊C4×C29—21no—
197C22⋊C4×C29—21no—
198C22⋊C4×C29—41no—
199C22⋊C4×C29—41no—
200C42×C29—41no—
201C42×C29—41no—
202C42×C29C2×D411yescharacteristic
203C42×C29C2×D411yescharacteristic
204C42×C29#4111yescharacteristic
205C42×C29C2411yescharacteristic
206#19562C2911yesmaximal, characteristic, direct product factor, Sylow
207C23×C29—21no—
208C23×C29—21no—
209C23×C29#12111yescharacteristic
210Q8×C29—41no—
211Q8×C29—41no—
212Q8×C29—41no—
213Q8×C29—41no—
214Q8×C29—81no—
215Q8×C29—81no—
216Q8×C29—81no—
217D4×C29—21no—
218D4×C29—21no—
219D4×C29—21no—
220D4×C29—21no—
221D4×C29—42no—
222D4×C29—81no—
223D4×C29—81no—
224D4×C29—81no—
225C2×C4×C29—21no—
226C2×C4×C29—21no—
227C2×C4×C29—21no—
228C2×C4×C29—21no—
229C2×C4×C29—21no—
230C2×C4×C29—21no—
231C2×C4×C29—41no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
236C2×C4×C29—41no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—41no—
240C2×C4×C29#12111yescharacteristic
241C2×C4×C29#12111yescharacteristic
242C2×C4×C29#12111yescharacteristic
243C2×C4×C29C22×D411yescharacteristic
244C2×C4×C29C22×D411yescharacteristic
245C2×C4×C29C2×#4111yescharacteristic
246C8×C29—21no—
247C8×C29—21no—
248C8×C29—21no—
249C8×C29—21no—
250C8×C29—41no—
251C8×C29—41no—
252C8×C29—41no—
253C8×C29—41no—
254C8×C29—41no—
255C8×C29—41no—
256#3246C2×C2911yescharacteristic
257#3235C2×C2911yescharacteristic
258#3231C2×C2911yescharacteristic, complemented
259#2979C2×C2911yescharacteristic
260#1703C2×C2911yescharacteristic, complemented
261#1699C2×C2911yescharacteristic, complemented
262#1695C2×C2911yescharacteristic, complemented
263#1691C2×C2911yescharacteristic, complemented
264#1683C2×C2911yescharacteristic, complemented
265#1679C2×C2911yescharacteristic, complemented
266#1675C2×C2911yescharacteristic, complemented
267#1671C2×C2911yescharacteristic, complemented
268#1573C2×C2911yescharacteristic, complemented
269#1554C2×C2911yescharacteristic, complemented
270#1542C2×C2911yescharacteristic, complemented
271C22×C29—21no—
272C22×C29—21no—
273C22×C29—21no—
274C22×C29—41no—
275C22×C29—41no—
276C22×C29—41no—
277C22×C29—41no—
278C22×C29—41no—
279C22×C29—41no—
280C22×C29C2×#12111yescharacteristic
281C4×C29—21no—
282C4×C29—21no—
283C4×C29—21no—
284C4×C29—21no—
285C4×C29—41no—
286C4×C29—41no—
287C4×C29—81no—
288C4×C29—81no—
289C4×C29—81no—
290C4×C29—81no—
291C4×C29#57711yescharacteristic
292C4×C29#57711yescharacteristic
293C4×C29#57711yescharacteristic
294C4×C29#57811yescharacteristic
295#533C22×C2911yescharacteristic
296#533C22×C2911yescharacteristic
297#532C22×C2911yescharacteristic
298#501—21no—
299#500C22×C2911yescharacteristic
300#498C22×C2911yescharacteristic
301#490—21no—
302#487C22×C2911yescharacteristic
303#487C22×C2911yescharacteristic
304#485—21no—
305#485—21no—
306#482—21no—
307#482—21no—
308#479—21no—
309#479—21no—
310#476C22×C2911yescharacteristic
311#476C22×C2911yescharacteristic
312#476C22×C2911yescharacteristic
313#476C22×C2911yescharacteristic
314#475—21no—
315#474C22×C2911yescharacteristic
316#474C22×C2911yescharacteristic
317#465—21no—
318#465—21no—
319#461C22×C2911yescharacteristic
320#461C22×C2911yescharacteristic
321#460—21no—
322#436—21no—
323#436C22×C2911yescharacteristic
324#436C22×C2911yescharacteristic
325C8×D4—21no—
326C8×D4C22×C2911yescharacteristic
327C8×D4C22×C2911yescharacteristic
328#432C22×C2911yescharacteristic
329#431C22×C2911yescharacteristic
330#431C22×C2911yescharacteristic
331C2×C4⋊C8C22×C2911yescharacteristic
332#408—21no—
333#408—21no—
334#335C22×C2911yescharacteristic
335#335C22×C2911yescharacteristic
336#334C22×C2911yescharacteristic
337#334C22×C2911yescharacteristic
338#333C22×C2911yescharacteristic
339#333C22×C2911yescharacteristic
340#333C22×C2911yescharacteristic
341#333C22×C2911yescharacteristic
342#332C22×C2911yescharacteristic
343#332C22×C2911yescharacteristic
344#332C22×C2911yescharacteristic
345#332C22×C2911yescharacteristic
346C2×C29—41no—
347C2×C29—81no—
348C2×C29—81no—
349C2×C29#304211yescharacteristic
350C2×C29#306311yescharacteristic
351C2×C29#306711yescharacteristic
352C2×#41—21no—
353C2×SD16—21no—
354C2×SD16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—21no—
360C4⋊Q8D4×C2911yescharacteristic
361C4⋊Q8C23×C2911yescharacteristic
362C4⋊Q8C23×C2911yescharacteristic
363C4⋊Q8C23×C2911yescharacteristic
364C4⋊Q8C23×C2911yescharacteristic
365#127D4×C2911yescharacteristic
366#125—21no—
367#125—21no—
368#124—21no—
369C22⋊Q8—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373#121—21no—
374#121D4×C2911yescharacteristic
375#121D4×C2911yescharacteristic
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×D4—21no—
381C4×D4C23×C2911yescharacteristic
382C4×D4C23×C2911yescharacteristic
383#117—21no—
384#117—21no—
385C2×C42C23×C2911yescharacteristic
386#107—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#106—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396C4⋊C8—21no—
397C4⋊C8D4×C2911yescharacteristic
398C4⋊C8D4×C2911yescharacteristic
399C4⋊C8C23×C2911yescharacteristic
400C4⋊C8C23×C2911yescharacteristic
401C4⋊C8C23×C2911yescharacteristic
402C4⋊C8C23×C2911yescharacteristic
403C4⋊C8C23×C2911yescharacteristic
404C4⋊C8C23×C2911yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8D4×C2911yescharacteristic
424C22⋊C8D4×C2911yescharacteristic
425#97—21no—
426C4×C8—21no—
427C4×C8C23×C2911yescharacteristic
428C4×C8C23×C2911yescharacteristic
429C29#1956211yescharacteristic, direct product factor, Sylow
430#41—81no—
431#41—81no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C2×D4×C2911yescharacteristic
442C2×D4C2×D4×C2911yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4C2×D4×C2911yescharacteristic
446C22×C4C2×D4×C2911yescharacteristic
447C22×C4#41×C2911yescharacteristic
448SD16—81no—
449SD16—81no—
450M16—81no—
451M16—81no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—81no—
459C2×C8—81no—
460C2×C8—81no—
461C2×C8C2×D4×C2911yescharacteristic
462C2×C8C2×D4×C2911yescharacteristic
463C2×C8C2×D4×C2911yescharacteristic
464C2×C8C2×D4×C2911yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4C2×D4×C2911yescharacteristic
479C4⋊C4C2×D4×C2911yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C42—41no—
487C42—41no—
488C42C2×D4×C2911yescharacteristic
489C42C2×D4×C2911yescharacteristic
490C42#41×C2911yescharacteristic
491C42C24×C2911yescharacteristic
492C23—21no—
493C23—21no—
494C23C29×#12111yescharacteristic
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—81no—
500Q8—81no—
501Q8—81no—
502D4—21no—
503D4—21no—
504D4—21no—
505D4—21no—
506D4—42no—
507D4—81no—
508D4—81no—
509D4—81no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4C29×#12111yescharacteristic
526C2×C4C29×#12111yescharacteristic
527C2×C4C29×#12111yescharacteristic
528C2×C4C22×D4×C2911yescharacteristic
529C2×C4C22×D4×C2911yescharacteristic
530C2×C4C2×#41×C2911yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—41no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22C2×C29×#12111yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—41no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4C29×#57711yescharacteristic
562C4C29×#57711yescharacteristic
563C4C29×#57711yescharacteristic
564C4C29×#57811yescharacteristic
565C2—41no—
566C2—81no—
567C2—81no—
568C2C29×#304211yescharacteristic
569C2C29×#306311yescharacteristic
570C2C29×#306711yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C29×#3231C2semidirect
5. C29×#1703C2semidirect
6. C29×#1699C2semidirect
7. C29×#1695C2semidirect
8. C29×#1691C2semidirect
9. C29×#1683C2semidirect
10. C29×#1679C2semidirect
11. C29×#1675C2semidirect
12. C29×#1671C2semidirect
13. C29×#1573C2semidirect
14. C29×#1554C2semidirect
15. C29×#1542C2semidirect
206. #19562C29direct (N × H)
258. #3231C2×C29semidirect
260. #1703C2×C29semidirect
261. #1699C2×C29semidirect
262. #1695C2×C29semidirect
263. #1691C2×C29semidirect
264. #1683C2×C29semidirect
265. #1679C2×C29semidirect
266. #1675C2×C29semidirect
267. #1671C2×C29semidirect
268. #1573C2×C29semidirect
269. #1554C2×C29semidirect
270. #1542C2×C29semidirect
429. C29#19562direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C29×#32462
C29×#32352
C29×#32312
C29×#29792
C29×#17032
C29×#16992
C29×#16952
C29×#16912
C29×#16832
C29×#16792
C29×#16752
C29×#16712
C29×#15732
C29×#15542
C29×#15422
#1956229